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Stuck on Manday questions

Boris and Sam can mow a garden in 4 hours. Boris can mow in 6 hours on his own. How long would Sam take on his own?

I am bit confused here so I haven’t done anything.
I’ll appreciate it if you can help me.
Thanks, Halime
(edited 1 year ago)

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Original post by Halime…
Boris and Sam can mow a garden in 4 hours. Boris can mow in 6 hours on his own. How long would Sam take on his own?

I am bit confused here so I haven’t done anything.
I’ll appreciate it if you can help me.
Thanks, Halime


If youre unsure how Sam and Boris combine their work, you could think about how much of the garden Boris would cut in the given time, so how much Sam must cut. Then think about how long it would take Sam to cut the whole garden.
Original post by mqb2766
If youre unsure how Sam and Boris combine their work, you could think about how much of the garden Boris would cut in the given time, so how much Sam must cut. Then think about how long it would take Sam to cut the whole garden.


Is it 8hrs?
I am very confused with this question. I don’t know how to work this out please show me working.
Thank you, Halime
(edited 1 year ago)
Original post by Halime…
8hrs I am very confused with this question I don’t know how to work this out please show me working. Thank you


sorry thats not how the forum works. The previous post should be enough for you to give it an attempt. There are a few ways to approach it, so post your working/attempt if youre stuck.
(edited 1 year ago)
This is a classic question. Probably there is an example in your textbook.
If you still need additional help, here's the first line (there are more direct methods. but this is easier to parse in my head).

"Let x be the amount of work Sam can do in one hour, and y be the amount of work Boris can do in one hour."
(assuming the entire amount of work is 1)

Should accompany with mqb's hint.
(edited 1 year ago)
I got 10 by doing this:

4/6 + 4/x = 1
4x + 10 = 4x
10 = x
Original post by Halime…
I got 10 by doing this:

4/6 + 4/x = 1
...
4x + 10 = 4x
10 = x


I agree with the first line, though you need to be sure about how you came about it. However subbing x=10 into the left hand side of the first line does not give 1. So youve made a mistake or two in the bold working.

Note that sometimes thinking about what youre doing on "each line" is easier than trying to blindly/incorretly do algebra.
(edited 1 year ago)
Original post by mqb2766
I agree with the first line, though you need to be sure about how you came about it. However subbing x=10 into the left hand side of the first line does not give 1. So youve made a mistake or two in the bold working.

Note that sometimes thinking about what youre doing on "each line" is easier than trying to blindly/incorretly do algebra.


So you mean 10 is the answer?
Original post by Halime…
So you mean 10 is the answer?


If youve tried to check it as per the previous post, then (hopefully) you should have found its not the answer. Its easy to type numbers into a calculator (if necessary, with x=10) and verify if does not equal 1.
Original post by mqb2766
If youve tried to check it as per the previous post, then (hopefully) you should have found its not the answer. Its easy to type numbers into a calculator (if necessary, with x=10) and verify if does not equal 1.

I posted this question cause I am finding it hard.
So can you direct me how to do it and what is the answer, please?
As I have not got it right in the last few tries.
Original post by Halime…
I posted this question cause I am finding it hard.
So can you direct me how to do it and what is the answer, please?
As I have not got it right in the last few tries.


4/6 + 4/x = 1
is correct. So you should be able to say
4/x = ...
then x should be clear? Alternatively reason about it using words as per the previous post so what fractio of the field does Boris do, so what fraction must Sam do, so what is Sams speed?

Note if youre really unsure about solving for x, just try some sensible values for x.
(edited 1 year ago)
Reply 11
Sam is clearly not pulling his/her weight. Try working out how much of the garden Boris would cut in 4 hours given his speed of 1/6 garden per hour. The remainder of the garden must be cut by Sam in this 4 hour time period. From this info you can work out Sam’s speed and from that how long to cut the whole garden. I hate algebra
Original post by mqb2766
4/6 + 4/x = 1
is correct. So you should be able to say
4/x = ...
then x should be clear? Alternatively reason about it using words as per the previous post so what fractio of the field does Boris do, so what fraction must Sam do, so what is Sams speed?

Note if youre really unsure about solving for x, just try some sensible values for x.

I’ve done this much and can’t get it.
If I knew how to do it I wouldn't have asked😄
Can you explain what the answer is and how to work it out.
Original post by Halime…
I’ve done this much and can’t get it.
If I knew how to do it I wouldn't have asked😄
Can you explain what the answer is and how to work it out.

Once you've got to 46+4x=1\dfrac{4}{6} + \dfrac{4}{x} = 1 you can forget all about gardens and people and things and just concentrate on solving this equation for x. I would suggest simplifying the first fraction to make the numbers easier.

So you now have (something) + (4/x) = 1

What would you do now to isolate the (4/x) term?
Thank you. But none of you is not helping me. You are making me more confused than explaining it. I do not want to know “this what you are meant to do”. I just want the formula and answer.
(edited 1 year ago)
Original post by Halime…
Thank you. But none of you is not helping me. You are making me more confused than explaining it. I do not want to know “this what you are meant to do”. I just want the formula and answer.


As mentioned a few times, if you have the equation
4/6 + 4/x = 1
you must know what each term represents. So
* What fraction of the field does Boris do?
* So what fraction of the field must Sam cut in 4 hours
* So how long would it take Sam to cut the field completely?

Alterrnatively, try x=1,2,3,4,.... in your calculator and see which value of x gives
4/6 + 4/x
equal to 1.
Reply 16
Original post by Halime…
I’ve done this much and can’t get it.
If I knew how to do it I wouldn't have asked😄
Can you explain what the answer is and how to work it out.

This is a tricky question - most GCSE students would easily mess it up and not get your correct equation for x. Here's my approach:
Boris & Sam: 4 hours ~ 1 whole garden... so 1/4 of garden in 1 hour.
Boris: 6 hours ~ 1 whole garden... so 1/6 of garden in 1 hour.
Therefore Sam would mow (1/4 - 1/6) = 1/12 of garden in 1 hour... so on his own 12 hours ~ 1 whole garden.
Hope this clarifies things.
Original post by vc94
This is a tricky question - most GCSE students would easily mess it up and not get your correct equation for x. Here's my approach:
Boris & Sam: 4 hours ~ 1 whole garden... so 1/4 of garden in 1 hour.
Boris: 6 hours ~ 1 whole garden... so 1/6 of garden in 1 hour.
Therefore Sam would mow (1/4 - 1/6) = 1/12 of garden in 1 hour... so on his own 12 hours ~ 1 whole garden.
Hope this clarifies things.

Thank you so much for the clarification I appreciate your help. As well as explaining it so well
Original post by vc94
This is a tricky question - most GCSE students would easily mess it up and not get your correct equation for x. Here's my approach:
Boris & Sam: 4 hours ~ 1 whole garden... so 1/4 of garden in 1 hour.
Boris: 6 hours ~ 1 whole garden... so 1/6 of garden in 1 hour.
Therefore Sam would mow (1/4 - 1/6) = 1/12 of garden in 1 hour... so on his own 12 hours ~ 1 whole garden.
Hope this clarifies things.


Hiya,
Sorry to annoy you,
Can you help me with the question down below

https://share.icloud.com/photos/0d2j...C1jQMB9coDqZyw
Original post by Halime…
Hiya,
Sorry to annoy you,
Can you help me with the question down below

https://share.icloud.com/photos/0d2j...C1jQMB9coDqZyw

Not sure if it's just me but when I try to follow that link I get an error!

Can you upload a picture of the question here?

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